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Lecture Notes 2.C

# All of the above requirements are met by introducing

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Unformatted text preview: imitive, the interaction gate. ¶11. Fig. II.23 is the symbol for the interaction gate and its inverse. Figure¶12. The mirror (indicatedinteraction gate is be used to deflect a ball’scan compute 15. Universal: The by a solid dash) can universal because it path (a), introduce a sboth AND and introduce a delay (c), and realize nontrivial crossover (d). ideways shift (b), NOT. ¶13. Interconnections: However, we must make provisions for arbitrary interconnections in a planar grid. So need to implement signal crossover and control timing. Figure 16. The switch gate and its inverse. Input signal x is routed to one of two output paths depending on the value of the control signal, C. Figure 12. (a) Balls of radius l/sqrt(2) traveling on a unit grid. (b) Right-angle elastic collision between two 64 CHAPTER II. PHYSICS OF COMPUTATION balls. Figure 14 Billiard ball model realization of the interaction gate. All of the above requirements are met by introducing, in addition to collisions between two balls, collisions between a ball and a fixed plane mirror. In this way, one can easily deflect the trajectory of a ball (Figure 15a), shift it sideways (Figure 15b), introduce a delay of an arbitrary number of time steps (Figure 1 Sc), and guarantee correct signal crossover (Figure 15d). Of course, no special precautions need be taken for trivial crossover, where the logic or the timing are such that two balls cannot possibly be present at the same moment at the crossover point (cf. Figure 18 or 12a). Thus, in the billiard ball model a conservative-logic wire is realized as a potential ball path, as determined by the mirrors. Note that, since balls have finite diameter, both gates and wires require a certain clearance in order to function properly. As a consequence, the metric of the space in which its inverse. is embedded (here, we are Figure 13. (a) The interaction gate and (b) the circuit considering igureEuclidean plane) is interaction gate and (b) its inverse.” (Fredkin & F the II.23: “(a) The reflected i...
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